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A chiral model based on a gauge group SU(3)C×{}SU(3)L×{}U(1)X contains dilepton gauge bosons and new quarks with exotic charges-4/3 and +5/3. Although coincident at low energy with the standard model, in the extended theory the third quark family is treated differently from the first two, and anomaly cancellation requires that the number of families be equal to the number of quark colors.
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P.H. Frampton (1992) studied this question.
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